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Evolution, dynamics, and fixed points

Author

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  • Joosten, Reinoud

    (MERIT)

Abstract

Sign-compatible dynamics describe changes in the composition of a population driven by differences in fitness. A saturated equilibrium is a fixed point for sign-compatible dynamics where each subgroup with positive population share has highest fitness. An evolutionary stable equilibrium is a saturated equilibrium attracting all trajectories nearby, such that the Euclidean distance to it decreases monotonically. We address existence, multiplicity, and dynamical stability of fixed points of sign-compatible dynamics. A saturated equilibrium may be approximated by using a variable dimension restart algorithm for solving the nonlinear complementarity problem. Journal of Economic Literature Classification Numbers: C62, C68, C72, C73. Keywords: Sign-compatible population dynamics, saturated equilibrium, evolutionary stable equilibrium, dynamic stability, nonlinear complementarity problem.

Suggested Citation

  • Joosten, Reinoud, 1995. "Evolution, dynamics, and fixed points," Research Memorandum 005, Maastricht University, Maastricht Economic Research Institute on Innovation and Technology (MERIT).
  • Handle: RePEc:unm:umamer:1995005
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    1. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
    2. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
    3. Dow, Gregory K., 1986. "Stability analysis for profit-responsive selection mechanisms," Mathematical Social Sciences, Elsevier, vol. 12(2), pages 169-183, October.
    4. Gilboa, Itzhak & Matsui, Akihiko, 1992. "A model of random matching," Journal of Mathematical Economics, Elsevier, vol. 21(2), pages 185-197.
    5. Armen A. Alchian, 1950. "Uncertainty, Evolution, and Economic Theory," Journal of Political Economy, University of Chicago Press, vol. 58(3), pages 211-211.
    6. Bomze, I.M. & van Damme, E.E.C., 1990. "A dynamical characterization of evolutionarily stable states," Discussion Paper 1990-45, Tilburg University, Center for Economic Research.
    7. Hansen, Robert G. & Samuelson, William F., 1988. "Evolution in economic games," Journal of Economic Behavior & Organization, Elsevier, vol. 10(3), pages 315-338, October.
    8. Nachbar, John H., 1991. "A comment on 'evolution in economic games'," Journal of Economic Behavior & Organization, Elsevier, vol. 16(3), pages 355-360, December.
    9. van der Laan, G. & Talman, A.J.J., 1987. "Computing economic equilibria by variable dimension algorithms : State of the art," Research Memorandum FEW 270, Tilburg University, School of Economics and Management.
    10. Doup, T.M. & van der Laan, G. & Talman, A.J.J., 1984. "The (2n+1-2)-ray algorithm : A new simplicial algorithm to compute economic equilibria," Research Memorandum FEW 151, Tilburg University, School of Economics and Management.
    11. Smale, Steve, 1976. "A convergent process of price adjustment and global newton methods," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 107-120, July.
    12. Talman, A.J.J. & van der Laan, G., 1979. "A restart algorithm for computing fixed points without an extra dimension," Other publications TiSEM 1f2102f8-e6da-4e9c-a2ed-9, Tilburg University, School of Economics and Management.
    13. Mailath, George J., 1992. "Introduction: Symposium on evolutionary game theory," Journal of Economic Theory, Elsevier, vol. 57(2), pages 259-277, August.
    14. G. van der Laan & A. J. J. Talman & L. van der Heyden, 1987. "Simplicial Variable Dimension Algorithms for Solving the Nonlinear Complementarity Problem on a Product of Unit Simplices Using a General Labelling," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 377-397, August.
    15. Talman, A.J.J. & van der Laan, G. & Van der Heyden, L., 1987. "Variable dimension algorithms for solving the nonlinear complementarity problem on a product of unit simplices using general labelling," Other publications TiSEM fbe9ae2f-e01d-4eef-944c-6, Tilburg University, School of Economics and Management.
    16. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-666, May.
    17. Boylan, Richard T., 1990. "Laws of Large Numbers for Dynamical Systems with Randomly Matched Individuals," Working Papers 748, California Institute of Technology, Division of the Humanities and Social Sciences.
    18. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
    19. Sonnenschein, Hugo, 1973. "Do Walras' identity and continuity characterize the class of community excess demand functions?," Journal of Economic Theory, Elsevier, vol. 6(4), pages 345-354, August.
    20. Giovanni Dosi & Christopher Freeman & Richard Nelson & Gerarld Silverberg & Luc Soete (ed.), 1988. "Technical Change and Economic Theory," LEM Book Series, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy, number dosietal-1988, November.
    21. Sonnenschein, Hugo, 1972. "Market Excess Demand Functions," Econometrica, Econometric Society, vol. 40(3), pages 549-563, May.
    22. Saari, Donald G & Simon, Carl P, 1978. "Effective Price Mechanisms," Econometrica, Econometric Society, vol. 46(5), pages 1097-1125, September.
    23. Keenan, Donald, 1981. "Further remarks on the Global Newton method," Journal of Mathematical Economics, Elsevier, vol. 8(2), pages 159-165, July.
    24. Saari, Donald G, 1985. "Iterative Price Mechanisms," Econometrica, Econometric Society, vol. 53(5), pages 1117-1131, September.
    25. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 59-89.
    26. Boylan, Richard T., 1992. "Laws of large numbers for dynamical systems with randomly matched individuals," Journal of Economic Theory, Elsevier, vol. 57(2), pages 473-504, August.
    27. Dierker, Egbert, 1972. "Two Remarks on the Number of Equilibria of an Economy," Econometrica, Econometric Society, vol. 40(5), pages 951-953, September.
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    More about this item

    Keywords

    mathematical economics and econometrics;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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